Calling Sequence

Arguments

A p-by-p
matrix. It contains the principal factors: eigenvectors of
the correlation matrix V.

comprinc

a n-by-p
matrix. It contains the principal components. Each column
of this matrix is the M-orthogonal projection of individuals
onto principal axis. Each one of this columns is a linear
combination of the variables x1, ...,xp with maximum
variance under condition u'_i M^(-1)
u_i=1

lambda

is a p column vector. It contains
the eigenvalues of V, where
V is the correlation matrix.

tsquare

a n column vector. It contains the Hotelling's
T^2 statistic for each data point.

Description

The idea behind this method is to represent in an approximative
manner a cluster of n individuals in a smaller dimensional
subspace. In order to do that, it projects the cluster onto a
subspace. The choice of the k-dimensional projection subspace
is made in such a way that the distances in the projection have
a minimal deformation: we are looking for a k-dimensional
subspace such that the squares of the distances in the
projection is as big as possible (in fact in a projection,
distances can only stretch). In other words, inertia of the
projection onto the k dimensional subspace must be maximal.

To compute principal component analysis with standardized variables may use
princomp(wcenter(x,1)) or use the pca function.